Error: 'web' is not a valid database version in this edition of SQL Server

Today I attempted to deploy a database from my local SQL Server (SQL Server 2014) to Azure. Everything seemed to go well until the actual deployment stage. That failed, with the error in the topic.

I retried, and instead of 'web' I picked 'standard'. I got pretty much the same error. Someone on StakOverflow suggested installing "Cumulative Update Package 6", but that ended up not doing anything at all.

Eventually I stumbled across someone who said that 'web' and 'standard' are older versions, and that newer versions of SSMS would provide the correct options. So I downloaded the latest RCE for 2016, and this time I indeed was able to select one of the newer versions (basic, standard and premium).